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Full text of "Analytical Mechanics"

CHAPTER XII. IMPULSE  AND   MOMENTUM.
190.   Impulse.—It was stated at the beginning of Chapter VIII that when a force acts upon a body two entirely different mechanical results are produced which are called work and impulse.   The former is the result of the action of force in space.   The latter is the result of the action of force in time.    We have already discussed work.   Impulse is the subject of the present chapter.
191.   Measure of Impulse. — If a force which is constant both in direction and magnitude acts upon a particle the impulse which it imparts to the particle equals the product of the force by the time during which it acts.    Since time is a scalar while force is a vector, impulse is a vector which has the same direction as the force.    If L denotes the impulse which a constant force F imparts in the interval of time t, we can write
L=F-t                                   (10
When the force is variable in magnitude or in direction, or in both, we must consider the impulses imparted in infinitesimal intervals of time and add them up. Thus
dl= Fdt
and                               L= CTdt.                                  (I)
Jo
Substituting in the last equation mv for F we have
L = / mv dt
Jo
= m I  dv,
<J VQ
= mv — rav0,                                (II)
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